#668 - Kth Smallest Number in Multiplication Table

Hard • View on LeetCode • View on GitHub

Problem Description

Nearly everyone has used the Multiplication Table. The multiplication table of size m x n is an integer matrix mat where mat[i][j] == i * j (1-indexed).

Given three integers m, n, and k, return the kth smallest element in the m x n multiplication table.

Solution

/**
 * @param {number} m
 * @param {number} n
 * @param {number} k
 * @return {number}
 */
var findKthNumber = function(m, n, k) {
  let low = 1;
  let high = m * n;

  while (low < high) {
    const middle = Math.floor((low + high) / 2);
    if (helper(middle) < k) {
      low = middle + 1;
    } else {
      high = middle;
    }
  }

  return low;

  function helper(x) {
    let count = 0;
    for (let i = 1; i <= m; i++) {
      count += Math.min(Math.floor(x / i), n);
    }
    return count;
  }
};